Ultrasonic measurement of surface profile and average diameter of a tube

ABSTRACT

Disclosed is a system and method for ultrasonic measurement of the average diameter and surface profile of a tube. A calibration block is used to calibrate the average tube diameter, and a correction is applied to account for any temperature difference of the couplant between calibration and test measurements. By using a linear probe, or a single probe with a finely pitched helicoidal scan, errors in diameter measurement due to presence of surface pits may be compensated.

FIELD OF THE INVENTION

The invention relates to methods and devices for measuring thedimensions and mechanical properties of pipes, tubes and the like. Moreparticularly, it relates to an ultrasonic device and algorithm formeasuring the deviation from the nominal tube diameter, without makingany assumptions about the shape of the tube.

BACKGROUND OF THE INVENTION

The ideal cross-section of a pipe or tube is perfectly circular,providing maximum strength and ease of joining adjacent tubing sections.Methods of measuring deviation of tubes from roundness are known in theart.

Known roundness measurement methods are often performed using adisplacement transducer mounted between two location members whichcontact the surface of the tube and locate the transducer. As the tubeunder test is rotated with respect to the transducer and the locationmembers, the transducer measures a displacement which is a weightedcombination of the departures from roundness of the transducer and thecontact points of the two location members. The advantage of thisgeometrical arrangement is that the measurement can be done with justone transducer, precision rotary bearings are not required, the axis ofthe tube does not have to be accurately aligned to the axis of rotation,and access to only one side of the rotating tube is required.

Moore (J. Phys. E: Sci. Instrum. 22 (1989) 339-343 and U.S. Pat. No.5,077,908) has presented design considerations and algorithms for such ageometrical arrangement. However, Moore is silent on the use ofultrasound transducers, which have the advantage that they are able tosimultaneously measure the wall thickness and the deviation fromroundness of the tube under test. Furthermore, Moore's algorithms areapplied to a two-dimensional circular object with no consideration ofany profile variations in the third dimension, which is the axial lengthof the tube.

Glasscock (U.S. Pat. No. 7,386,416) teaches use of an ultrasonic probefor measuring wall thickness and ovality. However, Glasscock' s methodis capable of measuring only the maximum and minimum deviation from theaverage diameter of the tube, thereby calculating the ovality. FIG. 1Aillustrates an ovality measurement of a tube 4′ having a nominallycircular outer surface 2′. According to the method of Glasscock, amaximum diameter D_(max) and a minimum diameter D_(min) of tube 4′ maybe measured along two perpendicular axes, and tube 4′ is assumed to havean oval shape as illustrated in FIG. 1A.

FIG. 1B illustrates a roundness measurement of a tube 4 whose diameterhas non-oval deviations from an average circle 2, wherein average circle2 is a circle having the average diameter of tube 4. Tube 4 is a bettergeneral representation than tube 4′ of observed roundness deviations intubes. Note, however, that the deviations from roundness of tube 4 havebeen exaggerated for clarity of presentation. Tube 4 may becharacterized by the maximum diameter D_(max) and the minimum diameterD_(min), but measurement of deviations 8 from average circle 2 for allpositions around the circumference of tube 4 would provide a much bettercharacterization. Measurements of such other, non-oval, deviations fromroundness are not possible with the method of Glasscock.

In general, users wish to determine variations along the axial length ofthe average diameter of the tube, not merely the roundness profile whichis a measure of deviations from a nominal tube diameter. A problem ofultrasonic roundness methods in existing practice is that themeasurement of the average tube diameter has low precision, and there isno method to calibrate for higher accuracy. Moreover, ultrasonicmeasurement of tube diameter has been found to be dependent on thetemperature of the couplant fluid (usually water), and there is noexisting method to achieve adequate temperature compensation.

A general problem of ultrasonic roundness methods in existing practiceis that when a pit in the tube surface is encountered, the two locationmembers, being much larger than the pit, will not be influenced, whereasthe ultrasonic beam will probe the bottom of the pit. This leads to anoverestimate of the average diameter and an inaccurate roundnessmeasurement.

There therefore exists a need for an ultrasonic method capable ofmeasuring deviations from tube roundness as a function of axialposition, while at the same time providing an accurate measurement ofthe axial dependence of tube average diameter, the average diametermeasurement being calibrated, independent of temperature variations, andunaffected by the presence of pits in the tube surface.

A method and system for accurate measurement of roundness and calibratedaverage diameter has been disclosed in a related co-pending U.S. patentapplication Ser. No. 16/033,949 filed on the same day as the currentdisclosure. However, the co-pending disclosure does not teachcompensation of temperature variations of the couplant, nor does itteach compensation for the presence of pits in the tube surface.

SUMMARY OF THE INVENTION

It is a general objective of the present disclosure to have ameasurement system and an algorithm for roundness and average diameterwhich is capable of measuring the deviation from the nominal diameter ofa tube, without making any assumptions about the shape of the tube.

The objective is achieved by measuring diameters of a random polygonalshape and then calculating the deviations from an averaged circle havinga diameter equal to the average of all the diameter measurements.

The measurement system of the present disclosure uses ultrasoundtime-of-flight measurements to measure the diameter of the tube at asubstantial number of angles around the tube (angles ranging from 0° to360°.

The roundness algorithm of the present disclosure represents thefunctional dependence of diameter with angle as a sum of Fouriercomponents, each component being a harmonic representing an integernumber of undulations per revolution. The number of harmonics depends onthe measurement accuracy required. The roundness is then calculated fromthe deviation of the Fourier sum from the averaged circle.

Note that the roundness algorithm of the present disclosure does notmerely use the maximum and minimum diameters to determine the tubeovality. The roundness algorithm instead determines a number ofharmonics 0, 2, . . . N, where the harmonic 0 corresponds to thediameter of the averaged circle, harmonic 2 corresponds to the ovalitycomponent, and higher harmonics complete the definition of the actualmeasured tube diameter angular profile.

A novel aspect of the present invention is that the roundness algorithmis not based on the assumption that the circles are oval or round anddoes not use ovality to achieve the calculation of the thickness of thetube.

It is a further objective of the present disclosure to provide acalibration method allowing highly accurate measurements of the averagediameter. This objective is achieved by providing a calibration blockconfigured to provide the same ultrasonic path length as a perfectlyround tube having the nominal diameter.

A further objective is to provide a calibration method which isindependent of temperature variations of the couplant between thecalibration and the measurement. This objective is achieved bycorrecting the measurement with knowledge of the temperature dependenceof sound velocity in the couplant.

A further objective is to provide a measurement system wherein themeasurement of average diameter is not affected by the presence of pitsin the surface of the tube. This is achieved by providing a linearultrasonic probe and contact bars whose length in the tube's axialdirection is much greater than the dimension of a surface pit. Themeasurement of average diameter may then be based upon those ultrasonicbeams from the linear probe which are unaffected by presence of thepits.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic representation of an ovality measurement.

FIG. 1B is a schematic representation of a roundness measurement.

FIG. 2A is a schematic representation of a test measurement system forroundness profiling of a tube according to the present disclosure.

FIG. 2B is a schematic representation of parameters used fordetermination of the average diameter of a tube.

FIG. 3 shows a phase representation of the amplitude of undulations forthe first 4 harmonics, n=0, 1, 2, and 3.

FIG. 4 shows a phase representation of the amplitude of undulations forthe first 3 harmonics, n=0, 1, and 2, together with circular geometricrepresentations of the tube profiles corresponding to each harmonic.

FIG. 5A is a diagram of a calibration block according to the presentdisclosure.

FIG. 5B is a schematic representation of a calibration system accordingto the present disclosure.

FIG. 6A is a graph showing the temperature dependence of sound velocityin water.

FIG. 6B is a graph showing the dependence of measured tube radius on thewater temperature difference between calibration and measurement.

FIG. 7 is a diagram illustrating the principle of compensation of themeasurement of the average diameter.

FIG. 8 is a photograph of a representative pit on a tube surface.

FIG. 9 is a schematic representation of a measurement system showing theeffect of a pit in the tube surface.

FIG. 10 is a side view of a measurement system in the presence of a pit.

FIG. 11 is an illustration of geometry for measuring the depth of a pit.

FIG. 12 is a flowchart of a method of measuring a roundness profile andan average diameter of a tube according to the present disclosure.

FIG. 13 is a schematic representation of a measurement system formeasuring a roundness profile and an average diameter of a tubeaccording to the present disclosure.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENT

FIG. 2A is a schematic representation of a test measurement system 1according to the present disclosure, wherein test measurement system 1is used for measurement of roundness and average diameter of a tube 4having a tube axis 18. Note that the deviations from roundness of tube 4illustrated in FIG. 2 are not to scale, but have been exaggerated forthe purpose of presentation. An ultrasonic probe 10 emits an ultrasonicbeam 12 which measures time of flight (TOF) in a couplant fluid 16between ultrasonic probe 10 and the outer surface of tube 4. Ultrasonicprobe 10 may be a single probe or may be a linear probe array having thedirection of the linear array substantially parallel to the axis of tube4. In an embodiment, probe 10 may be a linear phased array probe having168 elements and an active length of 139 mm, but other probe types arepossible and all are within the scope of the present disclosure.Ultrasonic beam 12 may therefore be a single beam or a linearly scannedbeam with the scanning direction substantially parallel to axis 18.Support frames 6 a and 6 b support ultrasonic probe 10 by contactingtube 4 at lines of contact 8 a and 8 b respectively, wherein lines ofcontact 8 a and 8 b are substantially parallel to axis 18 and aredefined by the contact of contact bars 9 a and 9 b respectively with thesurface of tube 4. Lines of contact 8 a and 8 b each subtend an angle αwith respect to the direction of ultrasonic beam 12. Tube 4 is rotatedabout axis 18 as illustrated by an arrow 14, the rotation being effectedby rollers 7 a and 7 b, and the rotation of tube 4 being represented bya rotation angle θ which varies from 0 to 2π during a single revolutionof tube 4. Couplant fluid 16, which in an embodiment may be water, isretained in an enclosed space between probe 10, support frames 6 a and 6b and tube 4. With knowledge of the sound velocity in couplant fluid 16,a time of flight measurement between ultrasonic probe 10 and the outersurface of tube 4 may be converted to a displacement measurement m(θ).The roundness profile of tube 4 is represented by s(θ), which is thedependence on angle θ of the deviation between the outer surface of tube4 and an average circle 2.

FIG. 2B is a schematic representation of parameters used for measurementof average circle 2, wherein average circle 2 is a circle having adiameter D₁, which is the average diameter of tube 4. A line 106 a istangential at a line of contact 8 a′ on average circle 2 and a line 106b is tangential at a line of contact 8 b′ on average circle 2, whereinlines of contact 8 a′ and 8 b′ both subtend angle α with respect to thedirection of ultrasonic beam 12. Note that, under the assumption thatroundness deviations between tube 4 and average circle 2 are small,lines of contact 8 a′ and 8 b′ are close to, but not exactly equivalentto, lines of contact 8 a and 8 b shown in FIG. 2A. Lines 106 a and 106 bintersect at an intersection 19, and a distance h is the distancebetween intersection 19 and the active surface of probe 10. Adisplacement q(θ) is the sum of displacement measurement m(θ) anddistance h, and corresponds to the distance from intersection 19 to thesurface of tube 4.

In order to determine diameter Di, displacement q(θ) must be determinedfor all values of angle θ from 0 to 2π. It should be noted that distanceh has no effect on the roundness measurement, but it does influencemeasurement of average circle diameter D₁. The value of distance h isnot precisely known in practice. However by using a calibration blockhaving the nominal tube diameter, an accurate measurement of averagecircle diameter D₁ may be made. The principle of the calibration isdisclosed below with reference to equations (7), (8) and (9).

Displacement measurement q(θ) can be related with roundness profile s(θ)and the weighted roundness profile at the position of the two points ofcontact, s(θ−α) and s(θ+α), using the following equation:

$\begin{matrix}{{q(\theta)} = {{s(\theta)} - \frac{{s\left( {\theta - \alpha} \right)} + {s\left( {\theta + \alpha} \right)}}{2\; \cos \; \alpha}}} & (1)\end{matrix}$

The functions q(θ) and s(θ) can be represented by a sum of Fouriercomponents Q(n) and S(n), where n takes integer values known asharmonics, each harmonic representing the number of undulations perrevolution of tube 4. FIG. 3 is a phase representation of the normalizedamplitude of undulations for the first four harmonics, n=0, 1, 2 and 3.For simplicity in each case the initial phase is set to 0.

FIG. 4 shows the phase representation of the first three harmonics, n=0,1, and 2, together with circular geometric representations of the tubeprofiles corresponding to each harmonic. In the circularrepresentations, the circles with solid lines are representations ofaverage circle 2, while figures with broken lines represent profiles ofactual tube 4.

The first harmonic (n=0) corresponds to a perfect circle for which theamplitude is a constant value and the deviation s(θ) from roundness iszero all around the tube. The second harmonic (n=1) corresponds to aperfect circle which is not centered with respect to the axis ofrotation. The dotted circle in the circular representation of harmonicn=1 shows an offset of tube 4 in the Y axis. The third harmonic (n=2)corresponds to tube 4 having an elliptical (oval) cross-section. Thedotted ellipse in the circular representation of harmonic n=2 iscentered with respect to the average circle 2. Higher harmonics (n>2)(not shown in FIG. 4) represent higher order variations in s(θ),representing roundness deviations which are non-oval.

Using the Fourier components Q(n) and S(n), for n=0, 2, . . . N, where Nis the highest harmonic number, a harmonic sensitivity G(n) can bedefined as:

$\begin{matrix}{{G(n)} = \frac{Q(n)}{S(n)}} & (2)\end{matrix}$

where G(n) is the sensitivity of probe measurement Q(n) to the tubeprofile variation S(n) for the n^(th) harmonic. G(n) is given by:

$\begin{matrix}{{G(n)} = {1 - \frac{\cos \; n\; \alpha}{\cos \; \alpha}}} & (3)\end{matrix}$

Therefore:

$\begin{matrix}{{S(n)} = {\frac{Q(n)}{G(n)} = \frac{Q(n)}{1 - \frac{\cos \left( {n\; \alpha} \right)}{\cos \; \alpha}}}} & (4)\end{matrix}$

Note that since Q(n) is generally a complex number, S(n) is a complexnumber in phase with Q(n).

In order to calculate Q(n), a series of ultrasonic measurements q(k) ismade as tube 4 is rotated (θ varies from 0 to 2π), where k is thesampling number and θ=k δθ, where δθ is the angular increment betweensamples. Q(n) is then derived as

Q(n)=FFT{q(k)}  (5)

for k=1, 2, . . . K, where K is the number of samples in one revolutionof the tube, and where FFT{q(k)} is the Fast Fourier Transform (FFT) ofthe measurements q(k). The harmonics S(n) may then be calculated fromequations (4) and (5), and finally the roundness profile of tube 4 isobtained using the Inverse Fast Fourier Transform of all harmonics S(n):

s(k)=FFT¹ {S(n)}  (6)

where FFT ¹{S(n)} is the Inverse Fast Fourier Transform of S(n).

Note that not all harmonics can be used because those harmonics forwhich G(n) is very small may make the calculation unstable in thepresence of signal noise. In particular, the second harmonic (n=1)cannot be used because G(1) is zero (see equation (3)). However, thesecond harmonic represents the displacement of tube 4 from the center ofthe nominal circle, which is not important for determination ofroundness and average diameter. To avoid the problem of zero sensitivityfor the second harmonic, the sensitivity

$\frac{1}{G(1)} = 0$

for n=1 is set to for the Fourier Transform calculation.

In general, in order to obtain a precise profile of the outside surfaceof tube 4, it is necessary to have a large number of samples, meaning asmall angular increment δθ between samples. It is also necessary toavoid harmonics n for which sensitivity factor G(n) is small or zero.This may be achieved by careful selection of the angle α subtended bylines of contact 8 a and 8 b with respect to the direction of ultrasonicbeam 12. In an embodiment, α may be equal to 48°. In a secondembodiment, α may be equal to 42°. However any other value of a may beadvantageous, and all such values are within the scope of the presentdisclosure.

In order to avoid instabilities due to harmonics having small or zerosensitivity factor G(n), 1/G(n) may be set to zero for the FourierTransform calculation for all values of G(n) less than a lowersensitivity limit. In an embodiment, the lower sensitivity limit may be0.3, but other values of the lower sensitivity limit are possible, andall such values are within the scope of the present disclosure.

The Fourier Transform calculation may be performed for harmonics n=0, 1,2, . . . N, where N is the highest order harmonic allowed by the systemdesign. For example, if G(n)>0.3, then according to Eq. 3,1-cos(nα)/cos(α)>0.3. This relationship may be satisfied for somecombinations of α and N. In general, the value of N should be as largeas possible, and in any event should be greater than or equal to 6.Another design factor to consider is the size of the measuringmechanism. The larger the value of angle α, the larger the size of themeasuring mechanism. Therefore there is a compromise between the size ofthe mechanism and the highest achievable harmonic number N. In anembodiment, with α=48°, the highest order harmonic may be N=13, butother values of the highest order harmonic are possible, and all suchvalues are within the scope of the present disclosure.

It is important to note that the distances, S(n), Q(n), s(k) and q(k),and the angle α, are all referenced to the diameter D₁ of average circle2. With the assumption that the deviations from average circle 2 aresmall, only the first harmonic n=0 corresponds to the diameter ofaverage circle 2. However, the diameter of average circle 2 cannot beaccurately measured with test measurement system 1 because the exactlength of the couplant column between probe 10 and the surface of tube 4is difficult to measure, and the distance h (see FIG. 2B) is unknown.The inventors of the present disclosure have discovered that theaccuracy of the average diameter measurement can be significantlyimproved by performing a calibration with a calibration system 3 using acalibration block 40 as shown in FIGS. 5A and 5B. Calibration block 40is configured to allow stable and repeatable location on calibrationblock 40 of the measurement system comprising probe 10, support frames 6a and 6 b and contact bars 9 a and 9 b. Calibration block 40 is furtherconfigured so that when the measurement system is located on calibrationblock 40, the acoustic path length from probe 10 to the surface ofcalibration block 40 accurately corresponds to a length L, whereinlength L is the acoustic path length from probe 10 to a nominal circle 2a having a nominal diameter D₀ (see FIG. 5B). Note that nominal circle 2a, as defined by the geometry of calibration system 3, represents thenominal diameter of tube 4. However, nominal diameter D₀ may bedifferent from average diameter D₁, which is the average tube diameteras measured with test measurement system 1. As illustrated in FIG. 5B,calibration block 40 has a cross-section which is part of nominal circle2 a. However, those skilled in the art may devise various forms andconstructions of calibration block 40 in which the acoustic path lengthfrom probe 10 to the surface of calibration block 40 accuratelycorresponds to the length L, and all such forms and constructions arewithin the scope of the present disclosure.

Calibration according to the present disclosure is performed bymeasuring a calibration time of flight in couplant fluid 16 when probe10 is coupled to calibration block 40. Note that calibration block 40 isnot rotated during the calibration measurement. Probe 10 is then coupledto tube 4 which is rotated, and the measured average diameter D₁ (firstharmonic) is compensated according to the calibration time of flight.The calibration allows an accurate measurement of the first harmonic n=0corresponding to the actual average diameter D₁ of tube 4. The method ofcompensating the first harmonic according to the calibration time offlight is described below in connection with FIG. 7 and equations(7)-(11).

The inventors of the present disclosure have observed that compensationof the first harmonic may be inaccurate if the temperature of couplantfluid 16 during calibration with calibration system 3 differs from thetemperature of couplant fluid 16 during the measurement with testmeasurement system 1. FIG. 6A shows a curve 28 representing thedependence of sound velocity in water on the temperature of the water.Curve 28 is well known in the art. FIG. 6B shows calculations of theradius of average circle 2 obtained from the calibrated first harmonicwhen measuring a tube having a nominal radius of 8.075 inches. A line 30shows the calibrated radius of average circle 2 when the watertemperature is 20° C. for both the calibration and the measurement. Acurve 32 shows the calculated radius of average circle 2 as a functionof the temperature difference between the calibration temperature at 20°C. and the measurement temperature. It may be seen from FIG. 6B that a5° C. difference in water temperature causes an error of approximately1% in the calculated radius. In the method of the present disclosure,this error is substantially eliminated by measuring the watertemperature during calibration and during measurement, and using thevelocity dependence of curve 28 (FIG. 6A) to correctly convert the timeof flight measurements to displacement measurements (see equations (7),(8) and (9) below). Note that only the first harmonic is corrected forcouplant temperature. Correction of higher harmonics is not required.

FIG. 7 illustrates the principle of compensation of the measurement ofthe first harmonic n=0 with calibration block 40. FIG. 7 shows asuperposition of measurement parameters for calibration with calibrationblock 40 (having diameter D₀ and radius R₀) and subsequent measurementof tube 4 (having average diameter D₁ and average radius R₁). In FIG. 7,line 106 a is tangential at line of contact 8 a′ to both average circle2 and calibration block 40, and a line 106 b is tangential at line ofcontact 8 b′ to both average circle 2 and calibration block 40. Notethat axis 18 of average circle 2 may not coincide with the correspondingaxis 18 a of calibration block 40. Distances q₀ and q₁ are measured fromintersection 19 to average circle 2 and calibration block 40respectively. Therefore, the distance q₀-h represents a sound path 12 afrom the active surface of probe 10 to the surface of calibration block40, and the distance q₁-h represents the sound path 12 from the activesurface of probe 10 to the surface of tube 4. Sound paths 12 and 12 a,and the difference Δq between them, can be calculated with equations(7), (8) and (9) below:

q ₀ −h=TOF₀×V₀/2   (7)

q ₁ −h=TOF₁×V₁/2   (8)

Δq=q ₁ −q ₀=(TOF₁×V₁−TOF₀×V₀)/2   (9)

where TOF₀ is the complete time of flight in the sound path q₀-h, TOF₁is the complete time of flight in the sound path q₁-h, wherein TOF₁ isderived as the average time of flight measured during a completerotation of tube 4, V₀ is the sound velocity in couplant fluid 16 duringcalibration with calibration block 40, and V₁ is the sound velocity incouplant fluid 16 during measurement of tube 4. Note that V₀ and V₁ maybe different because the temperature of couplant fluid 16 may bedifferent for the two measurements. The following equation may bederived from the geometrical relationships shown in FIG. 7:

$\begin{matrix}{{D_{1} = {{2\; \Delta \; q\frac{\cos \; \alpha}{1 - {\cos \; \alpha}}} + D_{0}}},} & (10)\end{matrix}$

where D₀ is the diameter of calibration block 40 (corresponding to thenominal diameter of tube 4) and D₁ is the average diameter of tube 4(corresponding to the first harmonic n=0 that needs to be compensated).

Note that in equations (9) and (10) the dependence on unknown distance hhas been eliminated, allowing an accurate determination of averagediameter D₁.

From Equations (9) and (10), the following final expression is derived:

$\begin{matrix}{D_{1} = {{\left( {{{TOF}_{1} \times V_{1}} - {{TOF}_{0} \times V_{0}}} \right)\frac{\cos \; \alpha}{1 - {\cos \; \alpha}}} + D_{0}}} & (11)\end{matrix}$

Equation (11) allows calibration of the measurement of average diameterD₁ by using calibration block 40 and taking into account the effect oftemperature change.

It should be noted that the equipment and methods of the presentdisclosure are generally applied to tubes having substantial axiallength, and that the average diameter and roundness profile shouldtherefore be measured as a function of axial position. Such measurementsmay be made by axially translating tube 4 during the measurement and/orby axially scanning ultrasonic beam 12 from ultrasonic probe 10, whereinprobe 10 is configured as a linear array probe. In making suchmeasurements, it is assumed that the average diameter and roundnessprofile of the tube change slowly in the axial direction relative to theaxial lengths of ultrasonic probe 10 and contact bars 9 a and 9 b. Whilethis assumption is generally true, errors can occur if there are smallpits in the surface of tube 4. FIG. 8 is a photograph of a surface pitwhich is typically a result of the method of production of the tube. Thedimension p representing the axial length of the pit is typically 1 to10 mm. The depth of a pit is typically 1 to 3 mm.

FIG. 9 illustrates a situation where the outside surface of tube 4 has apit 20 whose dimension in the axial direction is less than the axiallength of probe 10 and contact bars 9 a and 9 b. As illustrated in FIG.9, when tube 4 is rotated so that pit 20 is under ultrasonic beam 12,ultrasonic beam 12 may be sufficiently focused to probe the depth of pit20. However, when tube 4 rotates so that pit 20 is under either contactbar 9 a or contact bar 9 b, the contact bar, being axially longer thanpit 20, will ride over pit 20 and the contact bar radial position willbe unaffected by pit 20. This situation violates the three point contactassumption inherent in equation (1), and therefore diameter D₁ ofaverage circle 2 will be overestimated at the axial location of pit 20.

FIG. 10 shows a side view of tube 4, ultrasonic probe 10, support frame6 a and contact bar 9 a. Ultrasonic probe 10 is longer in the axialdirection than pit 20, and emits multiple ultrasonic beams 12, some ofwhich probe the depth of pit 20 and others do not. Among ultrasonicbeams 12 there is an ultrasonic beam 12 a which probes a maximum depth dof pit 20 and which therefore has a maximum time of flight t_(max)between probe 10 and tube 4. Also among ultrasonic beams 12 there is anultrasonic beam 12 b which does not probe pit 20 and which has a minimumtime of flight t_(min) between probe 10 and tube 4. Note that under theassumption that the roundness profile varies slowly in the axialdirection, there will be multiple beams 12 b having substantially thesame minimum time of flight, corresponding to all those beams 12 whichdo not probe pit 20. Furthermore, under the assumption that theroundness profile varies slowly in the axial direction, the time offlight of those beams 12, such as beam 12 a, which do probe pit 20, maybe replaced by minimum time of flight t_(min) in order to obtain areconstructed surface profile rsp(θ) which represents the profile oftube 4 in the absence of pit 20.

In summary, roundness calculation errors due to the presence of pit 20may be corrected by using a linear array probe 10 emitting multipleultrasonic beams 12, determining a minimum time of flight of ultrasonicbeams 12, and calculating displacement measurement q(θ) based on theminimum time of flight for all axial positions along the length of probe10.

As an alternative to using a linear probe array, a single probe or asingle aperture of a probe array may be used in conjunction with ahelicoidal scan, in which case the times of flight of many adjacentscans may be axially compared and the minimum time of flight used tocalculate displacement measurement q(θ). The pitch of the helicoidalscan should be less than half the axial dimension of a typical pit intube 4.

FIG. 11 illustrates how the depth profile of the pit may be determinedas tube 4 is rotated. A true tube surface profile tsp(θ) at each axiallocation, which takes the pit profile into account, may then becalculated from the equation:

tsp(θ)=rsp(θ)−V₁[t(θ)−t_(min)(θ)]  (12)

wherein tsp(θ) is the radius of the true surface profile, rsp(θ) is theradius of the reconstructed surface profile, V₁ is the acoustic velocityin couplant 16, t(θ) is the time of flight corresponding to an apertureat the axial location, and t_(min)(θ) is the minimum time of flightcorresponding to beam 12 b measured by linear probe 10 at angle θ.

As shown in FIG. 11, the maximum depth d of pit 20 will be measured atan angle θ_(p), wherein t(θ_(p))=t_(max). In equation (12), variation ofV₁ with temperature is not important since very accurate measurement ofprofile tsp(θ) is not required.

Note that FIG. 10 illustrates the thickness D of tube 4, which may bemeasured as a function of angle θ and axial position by means of thetime of flight difference between ultrasonic beams 12 reflected from theouter surface of tube 4 and those reflected from inner surface of tube 4(not shown), and with knowledge of the acoustic velocity in the materialof tube 4. Thus, use of the ultrasonic method has the advantage thatboth the roundness and the tube thickness may be measured.

FIG. 12 is a flowchart of a method of measuring the roundness profileand average diameter of a tube according to the present disclosure.Steps 50, 52 and 54 are the steps of a calibration mode 90. In step 50,probe 10 is coupled to calibration block 40 so that the acoustic pathlength in couplant 16 between probe 10 and calibration block 40 is equalto the nominal acoustic path length L between probe 10 and nominalcircle 2 a. In step 52, calibration time of flight TOF₀ is measuredbetween probe 10 and the surface of calibration block 40, and thetemperature of couplant 16 is measured at the time of calibration. Instep 54, the calibration time of flight and couplant temperature arestored for use in subsequent test measurements.

A test mode measurement 92 on a tube workpiece begins at step 56, inwhich probe 10 is coupled to tube 4. In step 57 the couplant temperaturefor the test mode measurement is measured and stored. In step 58, aseries of ultrasonic measurements q(k) is made as tube 4 is rotated360°. The measurements are made as a function of axial position withlinear probe 10 having its axis parallel to the axis of tube 4, and foreach axial position q(k) is derived from the minimum time of flighttrain of all apertures of probe 10. In step 60, the n^(th) harmonicsQ(n) are derived from the Fast Fourier Transform of q(k), and thecorresponding harmonics of the tube profile, S(n), are then calculatedfrom equation (4). In step 62, the inverse FFT is applied to S(n) toderive the reconstructed surface profile s(k) of tube 4, which is theprofile in the absence of surface pits.

Steps 64 and 66 are steps of calibration and of corrections applied tos(k) to account for temperature differences and the presence of pits. Instep 64, the average tube diameter D₁ is calculated and temperaturecompensated in accordance with equation (11), using the calibration timeof flight TOF₀, the average time of flight TOF₁, and the different soundvelocities at the test couplant temperature and the calibration couplanttemperature. In step 66, the true surface profile, taking into accountthe presence of pits, is calculated from equation (12) based on thedifference between the measured TOF at each angle and axial position,and the minimum TOF at that angle for all apertures of linear probe 10.

FIG. 8 is a schematic representation of a measurement system 100 formeasuring the roundness profile and average diameter of a tube accordingto the present disclosure. Measurement system 100 comprises calibrationsystem 3 with probe 10 coupled to calibration block 40. A calibrationacquisition unit 77 acquires ultrasound signals from probe 10 andtransmits calibration TOF₀ to an average diameter calibrator 84. Atemperature compensation unit 72 obtains a calibration couplanttemperature measurement of couplant 16 during the calibrationmeasurement, and outputs a calibration sound velocity V₀ with input froma sound velocity vs temperature table 74.

Measurement system 100 further comprises test measurement system 1,which is deployed subsequent to the calibration measurement, and fromwhich linear probe 10 transmits data to a test acquisition unit 76 andto a linear probe TOF unit 78. Linear probe TOF unit 78 determines timesof flight for all apertures of linear probe 10 and transmits minimumTOF, t_(min)(θ), to test acquisition unit 76. Temperature compensationunit 72 obtains a test couplant temperature measurement of couplant 16during the test measurement, and outputs a test sound velocity V₁ withinput from sound velocity vs temperature table 74. Test acquisition unit76 acquires a series of ultrasonic measurements q(k) as tube 4 isrotated 360°, the values of q(k) being based on the minimum TOF,t_(min)(θ), for all axial positions along the length of probe 10. A FFTcalculation module 80 then performs a Fast Fourier Transform to obtainthe harmonics S(n) of the profile of tube 4, and an Inverse FFTcalculation module 82 performs an Inverse Fast Fourier Transform toobtain the reconstructed surface profile s(k) of tube 4, which is theprofile in the absence of surface pits. With input from linear probe TOFunit 78, a true surface profile calculator 86 uses equation (12) toproduce the true surface profile, which is the surface profile of tube 4taking into account the presence of pits.

An average diameter calibrator 84 calibrates the average diameter D₁(the first harmonic of s(k)) by means of equation (11), usingcalibration TOF₀ from calibration system 3 and calibration and testsound velocities V₀ and V₁ from temperature compensation unit 72.

Therefore the output from measurement system 100 is the true surfaceprofile and calibrated average diameter D₁.

Although the present invention has been described in relation toparticular embodiments thereof, it can be appreciated that variousdesigns can be conceived based on the teachings of the presentdisclosure, and all are within the scope of the present disclosure.

What is claimed is:
 1. A method of measuring a tube in a test mode, the tube having a tube outer surface, the method comprising the steps of: providing a measurement assembly configured to be mounted on the tube outer surface and to hold at least one ultrasonic probe, the probe is configured to emit an ultrasonic beam in a beam plane and to receive response signals from the tube outer surface, the probe being coupled to the tube outer surface with a test couplant made of a couplant material; causing relative rotation between the tube and the probe, the rotation being about a tube axis oriented along a tube axial direction, wherein an angle θ is an angle of rotation, and wherein the angle θ is between 0° and 360°; measuring ultrasonic time of flight measurements, TOF(k), between the probe and the tube outer surface, wherein k is a sampling number and θ=k δθ, wherein δθ is an angular rotation increment between each ultrasonic time of flight measurement; converting the ultrasonic time of flight measurements to distance measurements, q(k), using a known test couplant sound velocity; calculating a Fourier transform of q(k); deriving harmonics, S(n), where n=0, 2, 3, . . . N, where S(n) is a n^(th) harmonic of a tube outer surface profile, N is a highest harmonic number and n=0 corresponds to an average circle having an average diameter of the tube outer surface; calculating an inverse Fourier transform of S(n) to derive the tube outer surface profile; measuring a test couplant temperature; measuring a calibration time of flight in a calibration mode wherein the probe is coupled to a calibration block with a calibration couplant made of the couplant material and having a calibration couplant temperature; determining the average diameter based on the calibration couplant temperature and the test couplant temperature; and, calculating a roundness profile, wherein the roundness profile is a deviation of the tube outer surface profile from the average circle, the deviation being measured as a function of the angle θ.
 2. The method of claim 1 wherein the probe is supported by a first support frame connected to a first contact bar and a second support frame connected to a second contact bar, wherein the first contact bar and the second contact bar are in contact with the tube outer surface.
 3. The method of claim 2 wherein the calibration mode comprises the steps of: acoustically coupling the probe to the calibration block with the calibration couplant, wherein the probe is supported by the first support frame and the second support frame, and wherein the first contact bar and the second contact bar are in contact with a calibration block surface such that a calibration beam path between the probe and the calibration block surface corresponds to a nominal tube diameter; measuring the calibration time of flight in the calibration couplant from the probe to the calibration block surface and back to the probe; measuring the calibration couplant temperature; and, determining a calibration couplant sound velocity from a known couplant material sound velocity temperature dependence.
 4. The method of claim 3 wherein the beam plane intersects the tube axis, wherein the first contact bar and the second contact bar are in contact with the tube outer surface at a first contact line and a second contact line respectively, wherein a first plane joining the first contact line to the tube axis makes an angle −α with the beam plane, and wherein a second plane joining the second contact line to the tube axis makes an angle α with the beam plane.
 5. The method of claim 4 wherein the average diameter is calculated in accordance with the equation $D_{1} = {{\left( {{{TOF}_{1} \times V_{1}} - {{TOF}_{0} \times V_{0}}} \right)\frac{\cos \; \alpha}{1 - {\cos \; \alpha}}} + D_{0}}$ wherein D₁ is the average diameter, D₀ is the nominal tube diameter, TOF₀ is the calibration time of flight, TOF₁ is an average time of flight, wherein the average time of flight is the average of the ultrasonic time of flight measurements, V₀ is the calibration couplant sound velocity and V₁ is the test couplant sound velocity at the test couplant temperature.
 6. The method of claim 2 wherein the tube outer surface has at least one surface pit thereon, the surface pit having a pit axial length, wherein the first contact bar has a bar axial length and the second contact bar has the bar axial length, and wherein the bar axial length is greater than the pit axial length and the linear probe length is greater than the pit axial length.
 7. The method of claim 6 wherein the step of causing relative rotation includes simultaneously translating the tube in the axial direction thereby forming a helicoidal tube scan.
 8. The method of claim 7 wherein the ultrasonic probe is a single probe and the helicoidal tube scan has a helicoidal pitch which is less than half the pit axial length.
 9. The method of claim 6 wherein the ultrasonic probe is a linear probe having a plurality of elements configured as a plurality of transmission apertures and having a linear probe direction with a linear probe length oriented substantially parallel to the axial direction, wherein the plurality of transmission apertures measures a plurality of aperture times of flight between each aperture and the tube outer surface, and wherein there is a minimum aperture time of flight corresponding to each rotation angle θ.
 10. The method of claim 9 wherein each of the plurality of aperture times of flight is set equal to the minimum aperture time of flight corresponding to each rotation angle θ, and wherein a reconstructed surface profile is thereby derived, wherein the reconstructed surface profile is a profile of the tube outer surface in the absence of the at least one pit and a reconstructed tube diameter is the average tube diameter in the absence of the at least one pit.
 11. The method of claim 10 wherein a true surface profile at an axial location is calculated from the reconstructed surface profile, the plurality of aperture times of flight and the minimum aperture time of flight, wherein the true surface profile is an angular profile of the tube outer surface at the axial location, including the at least one pit.
 12. The method of claim 11 wherein the true surface profile at the axial location is calculated in accordance with the equation tsp(θ)=rsp(θ)−V₁·[t(θ)−t_(min)(θ)] wherein tsp(θ) is a radius of the true surface profile, rsp(θ) is a radius of the reconstructed surface profile, V₁ is the test couplant sound velocity, t(θ) is a one of the plurality of aperture times of flight corresponding to an aperture at the axial location, and t_(min)(θ) is the minimum aperture time of flight.
 13. The method of claim 1 wherein the couplant material is water.
 14. A measurement apparatus for measuring a tube having a tube outer surface, the apparatus comprising, at least one ultrasonic probe, the probe is configured to emit an ultrasonic beam in a beam plane and to receive response signals from the tube outer surface, the probe being coupled to the tube outer surface with a test couplant made of a couplant material; a measurement assembly configured to be mounted on the tube outer surface, to hold the probe and to cause a relative rotation between the probe and the tube outer surface, the rotation being about a tube axis along a tube axial direction, wherein an angle θ is an angle of rotation, and wherein the angle θ is between 0° and 360°; a test acquisition unit configured to measure ultrasonic time of flight measurements, TOF(k), between the probe and the tube outer surface, wherein k is a sampling number and θ=k δθ, wherein δθ is an angular rotation increment between each ultrasonic time of flight measurement, the test acquisition unit further configured to convert the ultrasonic time of flight measurements to distance measurements, q(k), using a known test couplant sound velocity; a Fourier transform calculation module configured to calculate a Fourier transform of q(k) and to derive harmonics, S(n), where n=0, 2, 3, . . . N, where S(n) is a n^(th) harmonic of a tube outer surface profile, N is a highest harmonic number, and n=0 corresponds to an average circle having an average diameter of the tube outer surface; an inverse Fourier transform calculation module configured to calculate an inverse Fourier transform of S(n) to derive the tube outer surface profile; a temperature compensator configured to measure a test couplant temperature; a calibration system configured to measure a calibration time of flight wherein the probe is coupled to a calibration block with a calibration couplant made of the couplant material and having a calibration couplant temperature; an average diameter calibrator configured to calculate the average diameter based on the calibration couplant temperature and the test couplant temperature; and, a surface profile calculator configured to calculate a roundness profile, wherein the roundness profile is a deviation of the tube outer surface profile from the average circle, the deviation being measured as a function of θ.
 15. The measurement apparatus of claim 14 wherein the Fourier transform is a fast Fourier transform and the inverse Fourier transform is an inverse fast Fourier transform.
 16. The measurement apparatus of claim 14, wherein the tube is configured to rotate about the tube axis, and the measurement assembly is configured to hold the probe still.
 17. The measurement apparatus of claim 14 wherein the measurement assembly further comprises a first support frame connected to a first contact bar and a second support frame connected to a second contact bar, wherein the first contact bar and the second contact bar are in contact with the tube outer surface at a first contact line and a second contact line respectively, wherein a first plane joining the first contact line to the tube axis makes an angle −α with the beam plane, and wherein a second plane joining the second contact line to the tube axis makes an angle α with the beam plane.
 18. The measurement apparatus of claim 17 further comprising a calibration module, the calibration module comprising: a calibration block, wherein during a calibration mode, the probe is coupled to the calibration block with the calibration couplant, wherein the probe is supported by the first support frame and the second support frame, and wherein the first contact bar and the second contact bar are in contact with a calibration block surface such that a calibration beam path in the beam plane between the probe and the calibration block surface corresponds to a nominal tube diameter; a calibration acquisition unit configured to measure the calibration time of flight from the probe to the calibration block surface and back to the probe; and, the temperature compensator configured to measure the calibration couplant temperature and to determine a calibration couplant sound velocity from a known couplant material sound velocity temperature dependence.
 19. The measurement apparatus of claim 18 further comprising an average diameter calibrator configured to calculate a calibrated average diameter in accordance with the equation $D_{1} = {{\left( {{{TOF}_{1} \times V_{1}} - {{TOF}_{0} \times V_{0}}} \right)\frac{\cos \; \alpha}{1 - {\cos \; \alpha}}} + D_{0}}$ wherein D₁ is the average diameter, D₀ is the nominal tube diameter, TOF₀ is the calibration time of flight, TOF₁ is an average time of flight, wherein the average time of flight is the average of the ultrasonic time of flight measurements, V₀ is the calibration couplant sound velocity and V₁ is the test couplant sound velocity at the test couplant temperature.
 20. The measurement apparatus of claim 14 wherein the tube is translated in the axial direction and the roundness profile and the average diameter are calculated for a series of axial positions.
 21. The measurement apparatus of claim 20 wherein the probe is a linear probe having a plurality of elements configured as a plurality of transmission apertures and having a linear probe direction with a linear probe length oriented substantially parallel to the axial direction, wherein the plurality of transmission apertures measures a plurality of aperture times of flight between each aperture and the tube outer surface, and wherein there is a minimum aperture time of flight corresponding to each rotation angle θ.
 22. The measurement apparatus of claim 21 wherein the tube outer surface has at least one surface pit thereon, the surface pit having a pit axial length, wherein the first contact bar has a bar axial length and the second contact bar has the bar axial length, and wherein the bar axial length is greater than the pit axial length and the linear probe length is greater than the pit axial length.
 23. The measurement apparatus of claim 22 wherein the test acquisition unit sets each of the plurality of aperture times of flight to be equal to the minimum aperture time of flight corresponding to each rotation angle θ, and wherein a reconstructed surface profile is thereby derived, wherein the reconstructed surface profile is a profile of the tube outer surface in the absence of the at least one pit and a reconstructed tube diameter is the average tube diameter in the absence of the at least one pit.
 24. The measurement apparatus of claim 23 wherein a true surface profile calculator calculates a true surface profile at an axial location from the reconstructed surface profile, the plurality of aperture times of flight and the minimum aperture time of flight, wherein the true surface profile is an angular profile of the tube outer surface at the axial location, including the at least one pit.
 25. The measurement apparatus of claim 24 wherein the true surface profile calculator calculates the true surface profile at the axial location in accordance with the equation tsp(θ)=rsp(θ)−V_(i)·[t(θ)−t_(min)(θ)] wherein tsp(θ) is a radius of the true surface profile, rsp(θ) is a radius of the reconstructed surface profile, V₁ is the test couplant sound velocity, t(θ) is a one of the plurality of aperture times of flight corresponding to an aperture at the axial location, and t_(min)(θ) is the minimum aperture time of flight.
 26. The measurement apparatus of claim 14 wherein the couplant material is water. 